IM2.1: Students graph linear inequalities in two variables and quadratics. They model data with linear equations.

IM2.1.1: Graph a linear inequality in two variables.

Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

IM2.1.2: Interpret given situations as functions in graphs, formulas, and words.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

IM2.1.3: Find a linear equation that models a data set using the median fit method and use the model to make predictions.

Least-Squares Best Fit Lines
Solving Using Trend Lines

IM2.1.4: Graph quadratic functions. Show and explain the effects on the graph of changing a coefficient in a quadratic function. Find and interpret the zeros and maximum or minimum value of quadratic functions.

Addition and Subtraction of Functions
Exponential Functions
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Translating and Scaling Functions
Translations
Zap It! Game

IM2.2: Students identify and describe types of triangles. They define and apply the trigonometric relations. Students apply theorems to triangles and circles.

IM2.2.1: Find the lengths and midpoints of line segments in one-or two-dimensional coordinate systems.

Distance Formula

IM2.2.4: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similarity in Right Triangles
Triangle Inequalities

IM2.2.5: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

Concurrent Lines, Medians, and Altitudes
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

IM2.2.6: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

Perimeters and Areas of Similar Figures
Similar Figures

IM2.2.7: Find measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

Area of Triangles

IM2.2.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and the hinge theorem.

Triangle Inequalities

IM2.2.10: Use special right triangles (30°-60°-90° and 45°-45°-90°) to solve problems.

Cosine Function
Sine Function
Tangent Function

IM2.2.11: Define and apply the trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) defined by angles of right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

IM2.2.12: Know and use the relationship sin²x + cos²x = 1.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

IM2.2.15: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

Chords and Arcs
Inscribed Angles

IM2.2.16: Prove theorems related to circles.

Inscribed Angles

IM2.2.17: Construct tangents to circles and circumscribe and inscribe circles.

Circumference and Area of Circles
Concurrent Lines, Medians, and Altitudes
Inscribed Angles

IM2.2.20: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

Circumference and Area of Circles
Inscribed Angles

IM2.3: Students interpret scatterplots and analyze correlation.

IM2.3.1: Describe the association between two variables by interpreting a scatterplot.

Correlation

IM2.3.2: Interpret correlation coefficients.

Correlation

IM2.3.3: Make predictions from the least squares regression line or its equation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

IM2.3.4: Understand that a correlation between two variables does not necessarily imply one directly causes the other.

Correlation

IM2.3.5: Understand the effects of outliers on correlation coefficients, on the least squares regression line, and on the interpretations of correlation coefficients and regression lines in real-life contexts.

Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode

IM2.4: Students construct probability distributions, understand fundamental probability concepts, and use counting principles.

IM2.4.1: Construct a probability distribution by simulation and use it to understand and analyze the probabilistic situation.

Polling: City

IM2.4.2: Explore the geometric, or waiting-time, distribution.

Geometric Probability
Polling: City

IM2.4.3: Understand fundamental concepts of probability (i.e., independent events, multiplication rule, expected value).

Independent and Dependent Events

IM2.4.5: Use the basic counting principle, combinations, and permutations to compute probabilities.

Binomial Probabilities
Permutations and Combinations

IM2.5: Students use graphs and networks as mathematical models and use matrices to solve problems.

IM2.5.6: Apply matrix operations to solve problems (i.e., row sums, scalar multiplication, addition, subtraction, and matrix multiplication).

Translations

IM2.5.7: Use matrices and inverse matrices to answer questions that involve systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

IM2.6: Students apply trigonometric ratios to right triangles.

IM2.6.1: Explore properties and applications of the sine, cosine, and tangent ratios for the lengths of sides of right triangles.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

IM2.7: Students use a variety of strategies to solve problems and develop and evaluate mathematical arguments and proofs.

IM2.7.1: Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Solving Equations on the Number Line

IM2.7.8: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution as the original. Understand that similar logic applies to solving systems of equations simultaneously.

Solving Linear Systems (Standard Form)